A polynomially searchable exponential neighbourhood for graph colouring

• Published in: The Journal of the Operational Research Society Vol. 56; no. 3; pp. 324 - 330
• Main Authors: Glass, C A, Prügel-Bennett, A
• Format: Journal Article
• Language: English
• Published: Basingstoke Taylor & Francis 01-03-2005; Palgrave Macmillan Press; Palgrave; Taylor & Francis Ltd
• Subjects: Algorithms; Applied sciences; Combinatorial optimization; Combinatorial permutations; Exact sciences and technology; exponential neighbourhood; Graph coloring; graph colouring; Graphs; Heuristic; Heuristics; Hybridity; local search; Mathematical permutation; Mathematical programming; Neighborhoods; Operational research. Management science; Operations research; Optimization; Optimization techniques; Polynomials; Problem solving; Studies; Theoretical Papers; Urban universities; Vertices; Local search; heuristics; Permutation; Heuristic method; Neighbourhood; Subgraph; exponential neighbourhood; Graph colouring; Iterative method; Optimization
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/palgrave.jors.2601815

In this paper, we develop a new graph colouring strategy. Our heuristic is an example of a so-called polynomially searchable exponential neighbourhood approach. The neighbourhood is that of permutations of the colours of vertices of a subgraph. Our approach provides a solution method for colouring problems with edge weights. Results for initial tests on unweighted K-colouring benchmark problems are presented. Our colour permutation move was found in practice to be too slow to justify its use on these problems. By contrast, our implementation of iterative descent, which incorporates a permutation kickback move, performed extremely well. Moreover, our approach may yet prove valuable for weighted K-colouring. In addition, our approach offers an improved measure of the distance between colourings of a graph.